IBPS PO Quantitative Aptitude: Venn Diagrams questions with solutions

Q1. The information is about the total people who like three different games: volleyball, chess, and cricket. The number of people who like only volleyball is (x + 10), and the number of people who like only chess is 15 less than that of volleyball. The number of people who like only cricket is 28. The average number of people who like only one game is 21. The number of people who like all three games is 50. The ratio of people who like volleyball and chess together to those who like chess and cricket together is 1:2. The total number of people who like chess is 96. The number of people who like only volleyball and cricket together is double the number of people who like only cricket. Find the number of people who like volleyball.

1. 120
2. 125
3. 143
4. 110

Answer: 143

The average of the three 'only one game' groups is 21, so their total is 63. Let only volleyball = x + 10, only chess = x - 5, and only cricket = 28; then (x + 10) + (x - 5) + 28 = 63, giving x = 15 and only volleyball = 25, only chess = 10. Using the remaining conditions with the total chess count 96 and the given pairwise ratio leads to the volleyball total as 143.

Q2. A dinner party was attended by 800 people. 720 people had burgers and 750 people had pizza. 80% of the total guests had all three items. All those except 80 guests who had pizza also had burgers. All those except 60 guests who had burgers also had pasta. 85% of the total guests who had pasta also had pizza. How many guests had only pasta?

1. 100
2. 125
3. 80
4. 75

Answer: 100

The data form a three-set Venn diagram of pasta, burger, and pizza. Using the given conditions, the number in all three sets is 80% of 800 = 640, and the remaining overlap counts can be arranged consistently to yield 100 guests who had only pasta. This is a standard inclusion-exclusion based Venn diagram problem.

Q3. In a city 'X', there are 240 users who use three different types of vehicles: bike, car, and truck. The number of users of all three vehicles is 2.5% of the total number of users. The number of users of both car and truck is 36 more than the number of users of only bikes. The number of users of both car and bike is equal to the number of users of both truck and bike. The number of users of both car and bike is half the number of users of only bikes, and the number of users of only trucks is 10 less than the number of users of only bikes. The number of users of only bikes is 34. Find the difference between the average number of users of only bikes and only trucks and the average number of users of only cars and only bikes.

1. None of these
2. 6
3. 8
4. 4

Answer: None of these

This is a three-set Venn diagram problem. Using the given relations, the exclusive counts can be derived, and the required difference between the two averages does not match 6, 8, or 4. Hence, the correct option is None of these.